Low frequency thermal stability of the TianQin inertial sensor

Temperature fluctuation is a major disturbance for the space-based gravitational wave detectors, especially for the strain sensitivity of the TianQin inertial sensor. Comprehensive low-frequency thermal stability of the inertial sensor are essential inputs to the thermal design and the thermal diagnostics. However, the relative contributions of the different heat transfer effects within the vacuum chamber, as well as the effect of rarefied gas, remain undefined. In this work, the various heat transfer processes are decoupled and analyzed, particularly the rarefied gas heat transfer based on the frequency domain thermal framework. The results indicate that the thermal radiation accounts for only 4.55 % of the total heat transfer within the inertial sensor, and the rarefied gas heat transfer contributes even less. In order to meet the error budget, the temperature fluctuations along the x-axis direction of the vacuum chamber in the inertial sensor should be limited to 1 mK/Hz^1/2. Moreover, the thermocouples on the vacuum chamber should be arranged in pairs.